Combining reinforcement learning with mathematical programming:An approach for optimal design of heat exchanger networks

Heat integration is important for energy-saving in the process industry.It is linked to the persistently challenging task of optimal design of heat exchanger networks(HEN).Due to the inherent highly nonconvex nonlinear and combinatorial nature of the HEN problem,it is not easy to find solutions of high quality for large-scale problems.The reinforcement learning(RL)method,which learns strategies through ongoing exploration and exploitation,reveals advantages in such area.However,due to the complexity of the HEN design problem,the RL method for HEN should be dedicated and designed.A hybrid strategy combining RL with mathematical programming is proposed to take better advantage of both methods.An insightful state representation of the HEN structure as well as a customized reward function is introduced.A Q-learning algorithm is applied to update the HEN structure using theε-greedy strategy.Better results are obtained from three literature cases of different scales.

Study on Multi-stream Heat Exchanger Network Synthesis with Parallel Genetic/Simulated Annealing Algorithm

The multi-stream heat exchanger network synthesis (HENS) problem can be formulated as a mixed integer nonlinear programming model according to Yee et al. Its nonconvexity nature leads to existence of more than one optimum and computational difficulty for traditional algorithms to find the global optimum. Compared with deterministic algorithms, evolutionary computation provides a promising approach to tackle this problem. In this paper, a mathematical model of multi-stream heat exchangers network synthesis problem is setup. Different from the assumption of isothermal mixing of stream splits and thus linearity constraints of Yee et al., non-isothermal mixing is supported. As a consequence, nonlinear constraints are resulted and nonconvexity of the objective function is added. To solve the mathematical model, an algorithm named GA/SA (parallel genetic/simulated annealing algorithm) is detailed for application to the multi-stream heat exchanger network synthesis problem. The performance of the proposed approach is demonstrated with three examples and the obtained solutions indicate the presented approach is effective for multi-stream HENS.

Synthesis of Large-scale Multistream Heat Exchanger Networks Based on Stream Pseudo Temperature

Effective temperature level of stream, namely stream pseudo temperature, is determined by its actual temperature and heat transfer temperature difference contribution value. Heat transfer temperature difference con-tribution value of a stream depends on its heat transfer film coefficient, cost per unit heat transfer area, actual tem-perature, and so on. In the determination of the suitable heat transfer temperature difference contribution values of the stream, the total annual cost of multistream heat exchanger network (MSHEN) is regarded as an objective func-tion, and genetic/simulated annealing algorithm (GA/SA) is adopted for optimizing the heat transfer temperature difference contribution values of the stream. The stream pseudo temperatures are subsequently obtained. On the ba-sis of stream pseudo temperature, optimized MSHEN can be attained by the temperature-enthalpy (T-H) diagram method. This approach is characterized with fewer decision variables and higher feasibility of solutions. The calcu-lation efficiency of GA/SA can be remarkably enhanced by this approach and more probability is shown in search-ing the global optimum solution. Hence this approach is presented for solving industrial-sized MSHEN which is difficult to deal by traditional algorithm. Moreover, in the optimization of stream heat transfer temperature differ-ence contribution values, the effects of the stream temperature, the heat transfer film coefficient, and the construc-tion material of heat exchangers are considered, therefore this approach can be used to optimize and design heat exchanger network (HEN) with unequal heat transfer film coefficients and different of construction materials. The performance of the proposed approach has been demonstrated with three examples and the obtained solutions are compared with those available in literatures. The results show that the large-scale MSHEN synthesis problems can be solved to obtain good solutions with the modest computational effort.

Design of heat exchanger network based on entransy theory

The heat exchanger network(HEN) synthesis problem based on entransy theory is analyzed. According to the characteristics of entransy representation of thermal potential energy, the entransy dissipation represents the irreversibility of the heat transfer process, the temperature difference determines the entransy dissipation, and four HEN design steps based on entransy theory are put forward. The present study shows how it is possible to set energy targets based on entransy and achieve them with a network of heat exchangers by an example of heat exchanger network design for four streams. In order to verify the correctness of the heat exchanger networks design method based on entransy theory, the synthesis of the HEN for the diesel hydrogenation unit is studied. Using the heat exchange networks design method based on entransy theory, the HEN obtained is consistent with energy targets. The entransy transfer efficiency of HEN based on entransy theory is 92.29%, higher than the entransy transfer efficiency of the maximum heat recovery network based on pinch technology.

Method for Incorporation of Controllability in Heat Exchanger Network Synthesis by Integrating Mathematical Programming and Knowledge Engineering

A method for incorporation of controlling the heat exchanger networks with or without splits is proposed by integrating mathemati-cal programming and knowledge engineering. The simultaneous optimal mathematical model is established. This method can be practically used in the integration of large-scale heat exchanger networks, not only to synthesize automatically but also to satisfy the requirement of struc-tural controllability with more objective human intervention.

Strategy for Synthesis of Flexible Heat Exchanger Networks Embedded with System Reliability Analysis

System reliability can produce a strong influence on the performance of the heat exchanger network(HEN).In this paper,an optimization method with system reliability analysis for flexible HEN by genetic/simulated annealing algorithms(GA/SA) is presented.Initial flexible arrangements of HEN is received by pseudo-temperature enthalpy diagram.For determining system reliability of HEN,the connections of heat exchangers(HEXs) and independent subsystems in the HEN are analyzed by the connection sequence matrix(CSM),and the system reliability is measured by the independent subsystem including maximum number of HEXs in the HEN.As for the HEN that did not meet system reliability,HEN decoupling is applied and the independent subsystems in the HEN are changed by removing decoupling HEX,and thus the system reliability is elevated.After that,heat duty redistribution based on the relevant elements of the heat load loops and HEX areas are optimized in GA/SA.Then,the favorable network configuration,which matches both the most economical cost and system reliability criterion,is located.Moreover,particular features belonging to suitable decoupling HEX are extracted from calculations.Corresponding numerical example is presented to verify that the proposed strategy is effective to formulate optimal flexible HEN with system reliability measurement.

Synthesis of Heat Exchanger Network Considering Multipass Exchangers

Many methods have been proposed for synthesis of heat exchanger networks in recent years, most of which consider single pass exchangers. In this study some evolutionary rules have been proposed for synthesis of multipass exchanger networks. The method is based on the heuristic that optimal networks should feature maximum energy recovery and have the minimum number of shells. The effectiveness of the developed evolutionary rules is demonstrated through some literature examples.

Bypass Selection for Control of Heat Exchanger Network

Considering the flexibility and controllability of heat exchanger networks (HENs), bypasses are widely used for effective control of process stream target temperatures. However, the optimal location for the bypass is generally difficult to design with the trade-off between controllability and capital investments. In this paper, based on the steady-state model of heat exchanger networks the optimal bypass location was firstly selected by iteratively calculating the non-square Relative Gain Array (ns-RGA). To simplify the calculation process, rules of bypass selection were also proposed. In order to evaluate this method, then, the structural controllability of heat exchanger networks was analyzed. With both the consideration of the controllability and capital investments, the bypasses locations were finally selected. A case study on the HEN in Crude Distillation Unit was presented in which the ns-RGA and structural controllability were used to select bypasses and also to evaluate the results.

An Explicit Solution for Thermal Calculation and Synthesis of Super-structure Heat Exchanger Networks

For the optimal design of a heat exchanger network,the inlet and outlet stream temperatures of each heat exchanger in the network should be known.An explicit analytical solution of stream temperatures of an arbi-trary connected heat exchanger network was introduced,which is suitable for the thermal calculation of heat ex-changer networks.For the heat exchanger network synthesis,this solution was further developed and coupled with the stage-wise superstructure heat exchanger networks.The new calculation procedure reduced the computer mem-ory requirement dramatically.On the basis of this solution,a mathematical model for synthesis of heat exchanger networks with genetic algorithm was formulated,which is always feasible and no iteration is needed.Two examples were calculated with the proposed approach and better results were obtained.

Heat Exchanger Network Retrofit for Optimization of Crude Distillation Unit Using Pinch Analysis

Crude distillation unit(CDU)is regarded as the main energy consumer in the entire refinery process.In this paper,the process simulation software and the energy management software are used to simulate the flowsheet and analyze the energy consumption,respectively.Stream data obtained from an existing CDU are applicable in the pinch analysis.To reduce the amount of cross-pinch heat transfer,three approaches of resequencing,repiping,and adding heat exchangers are adopted.Compared with the existing CDU,the results demonstrate that the inlet temperature of the furnace can be increased by 25.4℃,the amount of hot and cold utilities can be reduced by 15.1%and 19.6%,respectively.The economic evaluation indicates that the operating cost is saved by 8×106$/a,and the payback period is about 9 months.

Heat Exchanger Network Retrofit of Diesel Hydrotreating Unit Using Pinch Analysis

Diesel hydrotreating unit(DHT)is an integral part of the refinery,and its energy-saving optimization is of great significance to the enterprise.In this paper,process simulation software and energy management software are used to simulate the flowsheet and analyze the energy consumption,respectively.Stream data obtained from an existing DHT are applied in the pinch analysis for retrofitting the heat exchanger network(HEN)to achieve maximum energy utilization by using pinch analysis.Since DHT is constrained by pressure,the pressure factor is considered in the process of retrofitting.The results show that the amount of cross-pinch heat transfer is reduced,the inlet temperature of the furnace is increased by 55℃,and the amount of hot and cold utilities can be reduced by 70.25%and 50.16%,respectively.The economic evaluation indicates that the operating cost is saved by 4.39×10^(6)$/a,and the payback period is about 2 months.

Flexibility analysis and design of heat exchanger network for syngas-to-methanol process

The heat exchanger network(HEN)in a syngas-to-methanol process was designed and optimized based on pinch technology under stable operating conditions to balance the energy consumption and economic gain.In actual industrial processes,fluctuations in production inevitably affect the stable operation of HENs.A flexibility analysis of the HEN was carried out to minimize such disturbances using the downstream paths method.The results show that two-third of the downstream paths cannot meet flexibility requirements,indicating that the HEN does not have enough flexibility to accommodate the disturbances in actual production.A flexible HEN was then designed with the method of dividing and subsequent merging of streams,which led to 13.89%and 20.82%reductions in energy consumption and total cost,respectively.Owing to the sufficient area margin and additional alternative heat exchangers,the flexible HEN was able to resist interference and maintain production stability and safety,with the total cost increasing by just 4.08%.

A systematic strategy for multi-period heat exchanger network retrofit under multiple practical restrictions

A systematic strategy for retrofit of the multi-period heat exchanger network （HEN） on the basis of the multi- objective optimization is developed. In this three-stage procedure, a simplified multi-objective optimization model of the multi-period lIEN is first established and then solved to target the retrofit, aiming to minimizing the total annual cost and total annual CO2 emissions. The obtained Pareto front represents series of retrofit targets under different emission limitations, from which the most desirable one can be selected. The matching of the existing and the required heat exchangers is further implemented to finalize the retrofit, which will meet the practical retrofit requirements and matching restrictions. The application of the proposed procedure is illustrated through a case study of a HEN in a vacuum gas oil hydro-treating unit.

Modeling and Optimization for Heat Exchanger Networks Synthesis Based on Expert System and Genetic Algorithm

A new superstructure form of heat exchanger networks (HEN) isproposed based on expert system system (ES). The new superstructureform is combined with the practical engineering. The differentinvestment cost formula for Different heat exchanger is alsopresented based on ES. The mathematical model for the simultaneousoptimization Of network configuration is established and solved by agenetic algorithm. This method can deal with larger scale HENsynthesis and the optimal HEN configuration is obtainedautomatically. Finally, a case study is presented to Demonstrate theeffectiveness of the method.

Combined mass and heat exchange network synthesis based on stage-wise superstructure model

Integrating multiple systems into one has become an important trend in Process Systems Engineering research field since there is strong demand from the modern industries. In this study, a stage-wise superstructurebased method is proposed to synthesize a combined mass and heat exchange network(CM&HEN) which has two parts as the mass exchange network(MEN) and heat exchange network(HEN) involved. To express the possible heat exchange requirements resulted from mass exchange operations, a so called "indistinct HEN superstructure(IHS)", which can contain the all potential matches between streams, is constructed at first. Then, a non-linear programming(NLP) mathematical model is established for the simultaneous synthesis and optimization of networks. Therein, the interaction between mass exchange and heat exchange is modeling formulated.The NLP model has later been examined using an example from literature, and the effectiveness of the proposed method has been demonstrated with the results.

Two-tier control structure design methodology applied to heat exchanger networks

Because of its paramount importance in the successful industrial control strategy of a given heat exchanger network(HEN),the control structure designs for providing appropriate manipulated variable(MV)and controlled variable pairings have received considerable attention.However,quite frequently HENs with such control structures face the problem of hard constraints,typically holding the HENs at less controlled operating space.So both the MV pairings and the above control pairings should be considered to design a control structure.This paper investigates the systematic incorporation of the two pairings,and presents a methodology for designing such two-tier control structure.This is developed based on the sequential strategy,coupling an indirect-tier with direct-tier control structure design,wherein the intention is realized in the former stage and the latter is implemented for further optimization.The MV identification and pairing are achieved through variations in heat load of heat exchangers to design the indirect-tier control structure.Then the direct-tier control structure is followed the relative gain array pairing rules.With the proposed methodology,on the one hand,it generates an explicit connection between the MV pairings and the HEN configuration,and the quantitative interaction measure is improved to avoid the multiple solutions to break the relationship among all the control pairings into individuals;on the other hand,a two-tier control structure reveals control potentials and control system design requirements,this may avoid complex and economically unfavourable control and HEN structures.The application of proposed framework is illustrated with two cases involving the dynamic simulation analysis,the quantitative assessment and the random test.

Synthesis of Flexible Heat Exchanger Networks with Stream Splits Based on Rangers of Stream Supply Temperatures and Heat Capacity Flowrates

A new superstructure model of heat exchanger networks (HEN) with streamsplits based on rangers of streams supply temperatures and heat capacity flow rates is presented.The simultaneous optimal mathematical model of flexible HEN synthesis is established too. Firstly,the streams with rangers of supply temperatures and/or the streams with the rangers of heat capacityflow rates are pretreated; Secondly, several rules are proposed to establish the superstructuremodel of HEN with splits and the simultaneous optimal mathematical model of flexible HEN; Thirdly,the improving genetic algorithm is applied to solve the mathematical model established at the secondstep effectively, and the original optimal structure of HEN based on the maximum operation limitingcondition can be obtained easily; Finally, the rules of heat exchange unit merged and the heat loadof heat exchanger relaxed are presented, the flexible configuration of HEN satisfied the operationcondition between the upper and down bounds of supply temperature and heat capacity flow rates canbe obtained based on the original optimal structure of HEN by means of these rules. A case studydemonstrates the method presented in this paper is effective

Simultaneous synthesis of sub and above-ambient heat exchanger networks including expansion process based on an enhanced superstructure model

Synthesis of heat exchanger networks including expansion process is a complex task due to the involvement of both heat and work.A stream that expands through expanders can produce work and cold load,while expansion through valves barely affects heat integration.In addition,expansion through expanders at higher temperature produces more work,but consumes more hot utility.Therefore,there is a need to weigh work production and heat consumption.To this end,an enhanced stage-wise superstructure is proposed that involves synchronous optimization of expander/valve placement and heat integration for each pressure-change sub-stream in stages.A mixed-integer nonlinear programming(MINLP)model is established for synthesizing sub and aboveambient heat exchanger networks with multi-stream expansion,which explicitly considers the optimized selection of end-heaters and end-coolers to adjust temperature requirement.Our proposed method can commendably achieve the optimal selection of expanders and valves in a bid for minimizing exergy consumption and total annual cost.Four example studies are conducted with two distinct objective function(minimization of exergy consumption and total annual cost,respectively)to illustrate the feasibility and efficacy of the proposed method.

A Multi-Objective Optimization Approach for Heat Exchanger Network in Process Industries

To simultaneously improve the quantity and quality of heat recovery in a heat exchanger network(HEN),this study conducts a theory analysis based on the first and second laws of thermodynamics.Under the premise of maximizing the heat recovery quantity of HEN,Ġdiss is used as an evaluation index to optimize the quality of heat recovery.Meanwhile,the total annual cost(TAC)is considered as another optimization objective to ensure the economic feasibility of the HEN.A superstructure-based multi-objective mixed integer non-linear programming approach is put forward to solve the trade-off between minimizingĠdiss and minimizing TAC.This allows for the optimum HEN structure to be obtained.A well-studied example is solved to highlight the benefits of the proposed method.

A Survey on a Heat Exchangers Network to Decrease Energy Consumption by Using Pinch Technology

There are several ways to increase the efficiency of energy consumption and to decrease energy consumption. In this paper. the application of pinch technology in analysis of the heat exchangers network （HEN） in order to reduce the energy consumption in a thermal system is studied. Therefore, in this grass root design, the optimum value of △Tmin, is obtained about 10℃and area efficiency （a） is 0.95. The author also depicted the grid diagram and driving force plot for additional analysis. In order to increase the amount of energy saving, heat transfer from above to below the pinch point in the diagnosis stage is verified for all options including re-sequencing, re-piping, add heat exchanger and splitting of the flows. Results show that this network has a low potential of retrofit to decrease the energy consumption, which pinch principles are planned to optimize energy consumption of the unit. Regarding the results of pinch analysis, it is suggested that in order to reduce the energy consumption, no alternative changes in the heat exchangers network of the unit is required. The acquired results show that the constancy of network is completely confirmed by the high area efficiency infirmity of the heat exchanger to pass the pinch point and from of deriving force plot.